Two lines 1 x − 3 = 3 y + 1 = − 1 z − 6 and 7 x + 5 = − 6 y − 2 = 4 z − 3 intersect at the point R . The reflection of R in the x y - plane has coordinates:

Question

Two lines 1 x − 3 ​ = 3 y + 1 ​ = − 1 z − 6 ​ and 7 x + 5 ​ = − 6 y − 2 ​ = 4 z − 3 ​ intersect at the point R . The reflection of R in the x y - plane has coordinates:

TestHub · Accepted Answer

Let the coordinate of P with respect to line 1 x − 3 ​ = 3 y + 1 ​ = − 1 z − 6 ​ = λ 7 x + 5 ​ = − 6 y − 2 ​ = 4 z − 3 ​ = μ L 1 ​ = ( λ + 3 , 3 λ − 1 , − λ + 6 ) and coordinate of P w.r.t. line L 2 ​ = ( 7 μ − 5 , − 6 μ + 2 , 4 μ + 3 ) ∴ λ − 7 μ = − 8 , 3 λ + 6 μ = 3 , λ + 4 μ = 3 From above equation : λ = − 1 , μ = 1 ∴ Coordinate of point of intersection R = ( 2 , − 4 , 7 ) Image of R w.r.t. x y plane = ( 2 , − 4 , − 7 )

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